Subgroups — #22586374

Order 9088.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17986368	C₂	1	1	yes	maximal, characteristic
2	#17985777	C₂	1	1	yes	maximal, characteristic
3	#347×C₇₁	C₂	1	1	yes	maximal, characteristic
4	#14556128	C₄	1	1	yes	characteristic
5	#14556120	C₄	1	1	yes	characteristic
6	#14556068	—	2	1	no	—
7	#14556053	—	2	1	no	—
8	#14556053	—	2	1	no	—
9	M₃₂×C₇₁	—	2	1	no	—
10	#97×C₇₁	C₂²	1	1	yes	characteristic
11	C₂×Dic₁₄₂	—	2	1	no	—
12	C₄⋊Dic₇₁	—	2	1	no	—
13	C₄⋊Dic₇₁	—	4	1	no	—
14	Dic₇₁⋊C₄	—	4	1	no	—
15	C₇₁⋊C₁₆	—	2	2	no	—
16	C₂×C₈×C₇₁	D₄	1	1	yes	characteristic
17	C₂×C₈×C₇₁	D₄	1	1	yes	characteristic
18	C₄²×C₇₁	C₂×C₄	1	1	yes	characteristic
19	C₁₆×C₇₁	—	2	2	no	—
20	C₂×C₄×C₇₁	—	2	1	no	—
21	C₂×C₄×C₇₁	C₂²⋊C₄	1	1	yes	characteristic
22	C₂×Dic₇₁	—	4	1	no	—
23	C₂×Dic₇₁	—	4	1	no	—
24	Dic₁₄₂	—	4	1	no	—
25	Dic₁₄₂	—	4	1	no	—
26	C₈×C₇₁	—	2	1	no	—
27	C₈×C₇₁	—	2	1	no	—
28	C₂²×C₇₁	#100	1	1	yes	characteristic
29	C₄×C₇₁	—	4	1	no	—
30	C₄×C₇₁	#104	1	1	yes	characteristic
31	C₄×C₇₁	#104	1	1	yes	characteristic
32	Dic₇₁	—	8	1	no	—
33	Dic₇₁	—	8	1	no	—
34	C₂×C₇₁	—	2	1	no	—
35	C₂×C₇₁	#329	1	1	yes	characteristic
36	#1356	—	71	1	no	maximal, Sylow
37	C₇₁	#1356	1	1	yes	characteristic, complemented, Sylow
38	#491	—	71	1	no	—
39	#347	—	71	1	no	—
40	#347	D₇₁	1	1	yes	characteristic
41	C₄⋊Q₈	—	71	1	no	—
42	#125	—	71	1	no	—
43	M₃₂	—	2	1	no	—
44	M₃₂	—	142	1	no	—
45	#103	—	142	1	no	—
46	#103	—	142	1	no	—
47	#97	C₂×D₇₁	1	1	yes	characteristic
48	C₂×Q₈	—	142	1	no	—
49	C₂×C₈	D₂₈₄	1	1	yes	characteristic
50	C₂×C₈	C₂²⋊D₇₁	1	1	yes	characteristic
51	C₄⋊C₄	—	284	1	no	—
52	C₄⋊C₄	—	284	1	no	—
53	C₄⋊C₄	—	142	1	no	—
54	C₄²	C₄×D₇₁	1	1	yes	characteristic
55	C₁₆	—	2	2	no	—
56	C₁₆	—	142	2	no	—
57	Q₈	—	284	1	no	—
58	Q₈	—	284	1	no	—
59	C₂×C₄	—	2	1	no	—
60	C₂×C₄	—	284	1	no	—
61	C₂×C₄	—	284	1	no	—
62	C₂×C₄	(C₂×D₇₁)⋊C₄	1	1	yes	characteristic
63	C₈	—	2	1	no	—
64	C₈	—	2	1	no	—
65	C₂²	#14556044	1	1	yes	characteristic
66	C₄	—	4	1	no	—
67	C₄	—	568	1	no	—
68	C₄	—	568	1	no	—
69	C₄	#14556054	1	1	yes	characteristic
70	C₄	#14556056	1	1	yes	characteristic
71	C₂	—	2	1	no	—
72	C₂	#17985738	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#17985738
commutator	C₄²×C₇₁	C₂×C₄
Frattini	#97	C₂×D₇₁
Fitting	#347×C₇₁	C₂
socle	C₂×C₇₁	#329
hypercenter	#347	D₇₁
hypocenter	C₇₁	#1356
LCS	G ▷ C₄²×C₇₁ ▷ C₂×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #97 ◁ #347

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
37. C₇₁	#1356	semidirect